A politician has commissioned a survey of bluecollar and whi

A politician has commissioned a survey of blue-collar and white-collar employees in her constituency. The survey reveals that 250 out of 500 blue-collar workers intend to vote for her in the next election whereas 344 out of 800 white-collar workers intend to vote for her. She wants to know if the level of support differs between the two groups of workers.

Which test statistic should be used?

What is the value of the test statistic for this data?

What is the p-value corresponding to the value of the test statistic?

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate, Level of support is diffrent b/w them H1: p1 != p2
Test Statistic
Sample 1 : X1 =250, n1 =500, P1= X1/n1=0.5
Sample 2 : X2 =344, n2 =800, P2= X2/n2=0.43
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.457
Q^ Value For Proportion= 1-P^=0.543
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.5-0.43)/Sqrt((0.457*0.543(1/500+1/800))
Zo =2.465
| Zo | =2.465
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.465 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 2.4649 ) = 0.0137
Hence Value of P0.05 > 0.0137,Here we Reject Ho